International paper sizes

The international standard is ISO 216, which defines amongst
others, A4. ISO paper sizes are
all based on a single aspect ratio of the
square
root of two, or approximately 1:1.4142. Basing paper upon this ratio was
conceived by Georg Lichtenberg in
the eighteenth century,
made law in Germany in the 1920s, but did not reach its
culmination until the prevalence of photocopy machines from the 1960s made having all paper with
the same aspect ratio far more convenient in scaling than any other system.

The largest standard size, A0, has an area of 1 m². A1 is formed by cutting
a piece of A0 in half, which retains the aspect ratio. This particular
measurement system was chosen in order to allow folding of one standard size
into another, which cannot be accomplished with traditional paper sizes.

Brochures are made by using material at the next size up i.e. material at A3
is folded to make A4 brochures. Similarly, material at A4 is folded to make A5
brochures.

It also allows scaling without loss of image from one size to another. Thus
an A4 page can be enlarged to A3 and retain the exact proportions of the
original document. Office photocopiers in countries that use ISO 216 paper often
have one tray filled with A4 and another filled with A3. A simple method is
usually provided (e.g. one button press) to enlarge A4 to A3 or reduce A3 to A4.
Thus an A4 brochure when open is A3 and can be placed on the copier and either
printed directly onto the A3 paper or reduced to A4.

The ISO B series is a scaling of the A series; B1 is half way between A0 and
A1 in area. The C series, defined in ISO
269, is half way between the A and B series of the same number; for
instance, C0 is half way between A0 and B0. This way, C0 is slightly larger than
A0, and B0 slightly larger than C0. This was intended to allow one to fit inside
an envelope of the other. For instance, a letter written on A4 paper, the
standard for this role, fits inside a C4 envelope. A C4 envelope can fit inside
a B4 envelope.

The scalability also means that less paper (and hence money) is wasted by
printing companies.

The measurements in millimetres are more appropriate for determining the
aspect ratio of paper than the less-accurate measurement of book sizes in
centimetres. However, there is a tolerance factor that lengths of paper less
than 150 mm can have plus-or-minus 1.5 mm and still qualify for the size
designation. Lengths from 150 to 600 mm can have plus-or-minus 2 mm, while those
over 600 can have plus-or-minus 3 mm.

ISO 216 does not define any sizes larger than A0 and B0, but the German
standard DIN 476 puts a
factor in front of these. Thus paper designated 2A0 is twice the size of A0,
while 4A0 is four times A0.

Although A4 is the standard size in the rest of the world, it doesn't fit in
US three-ring binders (and there is a different standard for hole-punched
binders to go with the international papers as well). However, the rarer E5
paper is less than a millimetre taller than US Letter size, though it is about
five-eighths of an inch narrower. Photocopies from A4 to E5 are simply reduced
to 95%, while from E5 to A4 increased to 105%. And notice that, as A4 is the
standard size for international firms, their web sites (such as that of ISO
itself) are designed to be printed on such paper of greater length. Printing
them out without adjustment, on US Letter-size paper, prints the bottom of the
page on a second sheet.

Current U.S. loose paper sizes

Current standard sizes of U.S. paper are a subset of the traditional sizes
referred to below. Letter, legal, and ledger/tabloid are by far the most
commonly used of these for everyday activities.

There is an additional paper size to which the name "government-letter" was
given by the IEEE
Printer Working Group: the 8-by-10½ inch paper that is used in America for
children's writing and was prescribed by Herbert Hoover when he
was Secretary of
Commerce to be used for U.S. governmental forms. Apparently this would
enable discounts from purchase of paper for schools. As photocopy machines later
proliferated, citizens wanted to make photocopies of the forms, but as the
machines did not generally have this size paper in their bins, they could not do
so, thus Ronald Reagan had the U.S.
government switch to letter size. 8" × 10½" is still commonly used in
spiral-bound notebooks and the like.

U.S. paper sizes are currently standard in the United States, Mexico, and the Philippines. In Canada, U.S. Paper
sizes are a de facto standard. The government, however, uses a combination of
ISO paper sizes and CAN 2-9.60M “Paper Sizes for Correspondence” specifies P1
through P6 paper sizes, which are the U.S. paper sizes rounded to the nearest
half-centimeter [1].

Current U.S. paper sizes for tablets

The sizes listed above are for paper sold loosely in reams.
There are a large number of sizes of tablets of paper, that is, sheets of paper
kept from flying around by being bound at one edge, usually by a strip of
plastic. Often there is a pad of cardboard (or greyboard)
at the bottom of the stack. Such a tablet serves as a portable writing surface,
and the sheets have lines printed on them, usually in blue, to make writing in a
line easier. An older means of binding is to have the sheets stapled to the
cardboard along the top of the tablet; there is a line of perforated holes
across every page just below the top edge from which any page may be torn off.
Lastly, the pad of sheets each weakly stuck with adhesive to the sheet below,
trade-marked as "Stick-Em's," serve as a sort of tablet. Their size is 3 inches
square.

The significance of taking separate note of these sizes is that their
contents are just as likely to be photocopied and enlarged, of course onto loose
paper, as are the more standardized international sizes of paper.

"Letter pads" are of course 8½ by 11 inches, but the term "Legal pad" is
often used for pads of this size besides those of 8½ by 14 inches. There are
"Steno pads" (used by stenographers) of 6 by 9
inches, and pads for pre-school children of twice and four times this size, but
which have lines going the long way across the paper: 9 by 12 inches and 12 by
18 inches. For the latter use, there are also pads 10¾ by 13½ inches.

For varied commercial purposes, all sorts of sizes have been recently
observed: 4 by 5½ inches; 5 by 8 inches; 5-3/8 by 8-1/4 inches; 6 by 9½ inches;
7¼ by 9½ inches; and 7¾ by 9-7/8 inches.

The only "metric" paper in the shops where this observation was taken are a
few Chinese-made "composition books" for
children which are 190 mm by 247 mm, a slight modification from the 7¾ by 9¾
inch ones. But the holes in the sheets of any of theses tablets fit
American-standard binders.

Japanese paper sizes

The JIS defines
two main series of paper sizes. The JIS A-series is identical to the ISO
A-series, but with slightly different tolerances. The area of B-series paper is
1.5 times that of the corresponding A-paper, so the length ratio is
approximately 1.22 times the length of the corresponding A-series paper. The
aspect ratio of the paper is the same as for A-series paper. Both A- and
B-series paper is widely available in Japan and most photocopiers are loaded
with at least A4 and B4 paper.

There are also a number of traditional paper sizes, which are now used mostly
only by printers. The most common of these old series are the Shiroko-ban and
the Kiku paper sizes.

Traditional paper sizes

Traditionally, a number of different sizes were defined for large sheets of
paper, and paper sizes were defined by the sheet name and the number of times it
had been folded. Thus a full sheet of "Royal" paper was 25 × 20 inches, and "Royal Octavo" was this
size folded 3 times, so as to make eight sheets, and was thus 10 by 6¼
inches.

Imperial sizes were used in the United Kingdom and its territories. Some of
the base sizes were as follows:

Name

inches

mm

Ratio

Emperor

72 × 48

1829 × 1219

1.5

Antiquarian

53 × 31

1346 × 787

1.7097

Grand Eagle

42 × 28¾

1067 × 730

1.4609

Colombier

34½ × 23½

876 × 597

1.4681

Atlas*

34 × 26

864 × 660

1.3077

Imperial*

30 × 22

762 × 559

1.3636

Pinched Post

28½ × 14¾

724 × 375

1.9322

Elephant*

28 × 23

711 × 584

1.2174

Princess

28 × 21½

711 × 546

1.3023

Cartridge

26 × 21

660 × 533

1.2381

Royal*

25 × 20

635 × 508

1.25

Sheet and Half Post

23½ × 19½

597 × 495

1.2051

Medium*

23 × 18

584 × 457

1.2778

Demy*

22½ × 17½

572 × 445

1.2857

Large Post

21 × 16½

533 × 419

1.2727

20 × 15½

508 × 394

1.2903

Copy Draught

20 × 16

508 × 406

1.25

Crown*

20 × 15

508 × 381

1.3333

Post*

19¼ × 15½

489 × 394

1.2419

Foolscap*

17 × 13½

432 × 343

1.2593

Small Foolscap

16½ × 13¼

419 × 337

1.2453

Brief

16 × 13½

406 × 343

1.1852

Pott

15 × 12½

381 × 318

1.2

The sizes marked with an asterisk are used in the US.

The common divisions and their abbreviations include:

Name(s)

Abbr.

Folds

Pages

Folio

fo/f

1

2

Quarto

4to

2

4

Sexto or Sixmo

6to/6mo

3

6

Octavo

8vo

3

8

Duodecimo or Twelvemo

12mo

4

12

Sextodecimo or Sixteenmo

16mo

4

16

Foolscap Folio is often
referred to simply as 'Folio' or 'Foolscap'. Similarly, 'Quarto' is more
correctly 'Copy Draught Quarto'.

Many of these sizes were only used for making books (see bookbinding), and would
never have been offered for ordinary stationery purposes.

Paper thickness and density

Grammage

Throughout the world, except in regions using US paper sizes, the product of
thickness and density of paper is expressed in grams per square metre (g/m²). This
quantity is commonly called grammage in both English and French (ISO
536).

The unofficial unit symbol "gsm" instead of the official "g/m²" is also
occasionally encountered in English speaking countries. This may be a result of
typists not knowing how to enter a superscript 2, a character not labeled on
standard US and UK keyboards.

For example, a "20 pound ream of Letter paper" has a weight of only 5 pounds
because uncut dimensions are twice the cut dimensions. Since the cut dimensions
are 8½ in × 11 in, the uncut dimensions are 17 in × 22 in. Therefore paper
weight per area of this type of Letter is: